1 /* mpfr_log2 -- log base 2 2 3 Copyright 2001-2018 Free Software Foundation, Inc. 4 Contributed by the AriC and Caramba projects, INRIA. 5 6 This file is part of the GNU MPFR Library. 7 8 The GNU MPFR Library is free software; you can redistribute it and/or modify 9 it under the terms of the GNU Lesser General Public License as published by 10 the Free Software Foundation; either version 3 of the License, or (at your 11 option) any later version. 12 13 The GNU MPFR Library is distributed in the hope that it will be useful, but 14 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 15 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public 16 License for more details. 17 18 You should have received a copy of the GNU Lesser General Public License 19 along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see 20 http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc., 21 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */ 22 23 #define MPFR_NEED_LONGLONG_H 24 #include "mpfr-impl.h" 25 26 /* The computation of r=log2(a) 27 r=log2(a)=log(a)/log(2) */ 28 29 int 30 mpfr_log2 (mpfr_ptr r, mpfr_srcptr a, mpfr_rnd_t rnd_mode) 31 { 32 int inexact; 33 MPFR_SAVE_EXPO_DECL (expo); 34 35 MPFR_LOG_FUNC 36 (("a[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (a), mpfr_log_prec, a, rnd_mode), 37 ("r[%Pu]=%.*Rg inexact=%d", mpfr_get_prec (r), mpfr_log_prec, r, 38 inexact)); 39 40 if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (a))) 41 { 42 /* If a is NaN, the result is NaN */ 43 if (MPFR_IS_NAN (a)) 44 { 45 MPFR_SET_NAN (r); 46 MPFR_RET_NAN; 47 } 48 /* check for infinity before zero */ 49 else if (MPFR_IS_INF (a)) 50 { 51 if (MPFR_IS_NEG (a)) 52 /* log(-Inf) = NaN */ 53 { 54 MPFR_SET_NAN (r); 55 MPFR_RET_NAN; 56 } 57 else /* log(+Inf) = +Inf */ 58 { 59 MPFR_SET_INF (r); 60 MPFR_SET_POS (r); 61 MPFR_RET (0); 62 } 63 } 64 else /* a is zero */ 65 { 66 MPFR_ASSERTD (MPFR_IS_ZERO (a)); 67 MPFR_SET_INF (r); 68 MPFR_SET_NEG (r); 69 MPFR_SET_DIVBY0 (); 70 MPFR_RET (0); /* log2(0) is an exact -infinity */ 71 } 72 } 73 74 /* If a is negative, the result is NaN */ 75 if (MPFR_UNLIKELY (MPFR_IS_NEG (a))) 76 { 77 MPFR_SET_NAN (r); 78 MPFR_RET_NAN; 79 } 80 81 /* If a is 1, the result is 0 */ 82 if (MPFR_UNLIKELY (mpfr_cmp_ui (a, 1) == 0)) 83 { 84 MPFR_SET_ZERO (r); 85 MPFR_SET_POS (r); 86 MPFR_RET (0); /* only "normal" case where the result is exact */ 87 } 88 89 /* If a is 2^N, log2(a) is exact*/ 90 if (MPFR_UNLIKELY (mpfr_cmp_ui_2exp (a, 1, MPFR_GET_EXP (a) - 1) == 0)) 91 return mpfr_set_si(r, MPFR_GET_EXP (a) - 1, rnd_mode); 92 93 MPFR_SAVE_EXPO_MARK (expo); 94 95 /* General case */ 96 { 97 /* Declaration of the intermediary variable */ 98 mpfr_t t, tt; 99 /* Declaration of the size variable */ 100 mpfr_prec_t Ny = MPFR_PREC(r); /* target precision */ 101 mpfr_prec_t Nt; /* working precision */ 102 mpfr_exp_t err; /* error */ 103 MPFR_ZIV_DECL (loop); 104 105 /* compute the precision of intermediary variable */ 106 /* the optimal number of bits : see algorithms.tex */ 107 Nt = Ny + 3 + MPFR_INT_CEIL_LOG2 (Ny); 108 109 /* initialize of intermediary variable */ 110 mpfr_init2 (t, Nt); 111 mpfr_init2 (tt, Nt); 112 113 /* First computation of log2 */ 114 MPFR_ZIV_INIT (loop, Nt); 115 for (;;) 116 { 117 /* compute log2 */ 118 mpfr_const_log2(t,MPFR_RNDD); /* log(2) */ 119 mpfr_log(tt,a,MPFR_RNDN); /* log(a) */ 120 mpfr_div(t,tt,t,MPFR_RNDN); /* log(a)/log(2) */ 121 122 /* estimation of the error */ 123 err = Nt-3; 124 if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, Ny, rnd_mode))) 125 break; 126 127 /* actualization of the precision */ 128 MPFR_ZIV_NEXT (loop, Nt); 129 mpfr_set_prec (t, Nt); 130 mpfr_set_prec (tt, Nt); 131 } 132 MPFR_ZIV_FREE (loop); 133 134 inexact = mpfr_set (r, t, rnd_mode); 135 136 mpfr_clear (t); 137 mpfr_clear (tt); 138 } 139 140 MPFR_SAVE_EXPO_FREE (expo); 141 return mpfr_check_range (r, inexact, rnd_mode); 142 } 143